Current reactors (almost all Light Water Reactors, LWR) use solid fuel in complex fuel rod assemblies, most with water cooling. If water isn’t there to cool, fuel rods melt. LWR materials can’t handle the hottest the reactor could get if cooling fails, e.g. zirconium fuel rods oxidize at ~500°C, only 45% above normal temperature of ~350°C, releasing hydrogen from water, and further heating the fuel rods. At Fukushima, the hydrogen then exploded. If the LWR fuel rods get still hotter, the rods would melt, and the fuel could melt through the reactor vessel.
Steel reactor vessel and water cooling weren’t the best materials and cooling, just the best known, for finding out if controlled fission for power generation would work. Also, the first reactors of this type were for submarine propulsion, where water and steel made a lot of sense (small, well below the limits of steel, simple design; scaling up to commercial scale and maximizing temperatures for more electricity production that required the complexity). The designers thought commercial reactors should have better materials, better design. (For example, the patent holder on PWR, which includes LWR, ran Oak Ridge National Laboratories during the Molten Salt Reactor Experiment.)
The fuel in a LFTR is molten (a liquid, with no water), under normal operation. The fuel is chemically bonded to a salt coolant, that doesn’t evaporate (the salt won’t boil below ~1400°C, the reactor operating temperature likely between 600°-950°C).
Uranium molten in liquid fluoride salt is chemically stable (unlike sodium coolant in some types of reactors, sodium reacts explosively with air or water).
Materials in LFTR would be designed to safely handle the hottest the reactor could possibly get, in normal or emergency situations.
If a LFTR (or any Molten Salt Reactor) somehow overheats, a frozen plug melts and fuel drains harmlessly into passive cooling tanks, where further nuclear reaction is impossible. (Later can be re-heated and pumped back into the reactor, and the nuclear reaction re-starts.) The cooling tanks also would be made of materials that handle the hottest the fuel could get, and cool quickly to air or earth, no water or electricity needed.
Beyond the obvious “the fuel is already molten”, the fuel can’t melt through the reactor vessel and put radioactive material in the environment.
Even if the reactor vessel is damaged (e.g. terrorist bomb, or earthquake) the fuel would simply spill out (no high pressures, so no pressure explosion like LWR) and the fuel would remain in the salt. The fuel density would remain the same (unlike LWR fuel that would melt out of the fuel rods and become more dense), and would spread out and rapidly cool to solid. No fission. No water needed. No water spreading radioactive material. Too dense to be carried by air, doesn’t dissolve well in water, doesn’t interact with water.
Fuel and most fission products are chemically bound to the salt. Fission products that are gasses (krypton and xenon, mainly) get continuously collected, since they just bubble out of the molten salt, so there are minimal amounts of these in the reactor. The reactor would be continuously fueled, so there is just enough uranium in the reactor to maintain fission, much less than in LWR (which is usually 1/3 refueled every 18 months).